Non-linear structure formation in modified gravity models

Transcription

1 Non-linear structure formation in modified gravity models Kazuya Koyama Institute of Cosmology and Gravitation, University of Portsmouth

2 Curvature Assuming GR Psaltis Living Rev. Relativity 11 (2008), 9 Baker et.al Rsun 1 AU Grav Probe B Hulse-Taylor Moon Mercury 10 kpc Dark Matter 10 Mpc curvature GM R rc 3 2 potential GM 2 rc Dark Energy Gravitational potential

3 Curvature 1 Rsun 1 AU Grav Probe B General Relativity Moon Mercury Hulse-Taylor Dark Matter Screening mechanism 10 kpc 10 Mpc Cosmological tests of gravity Modified Gravity Gravitational potential

4 General picture Largest scales gravity is modified so that the universe accelerates without dark energy Large scale structure scales gravity is still modified by a fifth force from scalar graviton model independent tests of GR Small scales (solar system) 1 H 0 r * GR Linear scales Modified gravity Scalar tensor GR is recovered KK: arxiv:

5 How to recover GR on small scales? On non-liner scales, the fifth force must be screened by some mechanisms Chameleon mechanism Joyce, Jain, Khoury & Trodden arxiv: Khoury & Weltman Phys. Rev. Lett. 93 (2004) The mass of a scalar mode becomes large in dense regions Vainshtein mechanism Non-liner derivative self-interactions become large in a dense region i j 2 rc i j Ga 3 8

6 Behaviour of gravity There regimes of gravity GR Scalar tensor In most models, the scalar mode obeys non-linear equations describing the transition from the scalar tensor theory on large scales to GR on small scales g / cm, g / cm, 10 g / cm Understandings of non-linear clustering require N-body simulations where the non-linear scalar equation needs to be solved crit galaxy solar 3

7 N-body simulations GR superposition of forces F( r) m f ( r r ) i i i i Modified gravity models the non-linear nature of the scalar field equation implies that the superposition rule does not hold It is required to solve the non-linear scalar equation directly on a mesh a computational challenge! The breakdown of the superposition rule has interesting consequences

8 N-body Simulations (Puchwein s talk) Multi-level adaptive mesh refinement solve Poisson equation using a linear Gauss-Seidel relaxation add a scalar field solver using a non-linear Gauss Seidel relaxation ECOSMOG Li, Zhao, Teyssier, KK JCAP1201 (2012) 051 MG-GADGET Puchwein, Baldi, Springel MNRAS (2013) ISIS Llinares, Mota, Winther A&A (2014) 562 A78 DGPM, Schmidt PRD80, Modified Gravity Simulations comparison project Winther, Shcmidt, Barreira et.al. arxiv:

9 Redshift space distortions Power spectrum in redshift space is anisotropic P( k, ), k / k f(r) linear GR linear Multipole decomposition P( k, ) P ( k) L ( ) P P 2 0 f linear P P 4 4 f f f 3 5, v Jennings, Baugh, Li, Zhao, Koyama, f 2 f(r) GR Modelling of non-linear effects is crucial to extract the differences in the linear growth rate between GR and modified gravity models

10 Perturbation theory KK, Taruya, Hiramatsu PRD Taruya,KK, Hiramatsu, Oka, PRD Taruya et.al. PRD Peturbation theory based template (Taruya s talk) Scale dependent growth BOSS DR11 constraints 810 f R 0 Song, Taruya, Linder, KK et.al

11 How do we test gravity in cosmology? Newton potential controls dynamics of non relativistic particles Space curvature also deflects lights In GR there is a special relation between the two dynamical mass = lensing mass in GR

12 Where to test GR GR is recovered in high dense regions (we consider the chameleon mechanism here) GR is restored in massive dark matter halos Scalar tensor GR Environmental effects Even if dark matter halo itself is small, if it happens to live near massive halos, GR is recovered Using simulations, we can develop criteria to identify the places where GR is not recovered Zhao, Li, KK Phy. Rev. Lett. 107 (2011)

13 Environmental dependence Difference between lensing and dynamical mass d( r) / dr M ( r) 1, d ( r) / dr 2 environment: D d / r NB O(1) difference no difference O(1) difference no difference Zhao, Li, KK Phy. Rev. Lett. 107 (2011)

14 Testing chameleon gravity Outskirt of clusters Terukina. et.al. PRD , JCAP Mlens Mdyn M Dynamical mass can be inferred from X-ray and SZ 48 X-ray clusters from XCS compared with lensing (shear) from CFHTLS f R 0 5 Wilcok et.al. MNRAS ( )

15 Creating a screening map It is essential to find places where GR is not recovered Small galaxies in underdense regions SDSS galaxies within 200 Mpc Cabre, Vikram, Zhao, Jain, KK JCAP 1207 (2012) 034 (we consider the chameleon mechanism here) GR is recovered

16 Tests of gravity on small scales dwarf galaxies in voids strong modified gravity effects Galaxies are brighter Pulsers pulsate faster Various other tests Jain & VanderPlas JCAP 1110 (2011) 032 Hui, Nicolis & Stubbs Phys. Rev. D80 (2009) (we consider the chameleon mechanism here) Davis et.al. Phys. Rev. D85 (2012) Jain et.al. ApJ 779 (2013) 39 Vikram et.al. JCAP1308 (2013) f R 0 7

17 Constraints on chameleon gravity Lombriser et.al. PRD Jain et.al f R 0 Interaction range of the extra force that modifies GR in the cosmological background GR Non-linear regime is powerful for constraining chameleon gravity Astrophysical tests could give better constraints than the solar system tests and can be done by piggybacking ongoing surveys

18 Vainshtein mechanism Vainshtein mechanism is very efficient dark matter halos are all screened regardless of mass and environment Schmidt PRD linear/quasi non-linear scales are the best place to test the models Screening depends on dimensionality of the system lower dimensional objects are Voids less screened (Barreira, Cai s talk) Voids are unscreened by definition Falck et.al. JCAP Falck, Cautun, Zhao, KK in preparation Tangential velocity (Falck s talk) Radius

19 Summary In the next decade, we may be able to detect the failure of GR on cosmological scales Linear scales model independent tests of gravity SUMIRE Non-linear scales novel astrophysical tests of gravity (in a model dependent way) EUCLID It is required to develop theoretical models from fundamental theory